Arbitrage problems with reflected geometric Brownian motion

Buckner, Dean; Dowd, Kevin; Hulley, Hardy

Abstract

Contrary to the claims made by several authors, a financial market model in which the price of a risky security follows a reflected geometric Brownian motion is not arbitrage-free. In fact, such models violate even the weakest no-arbitrage condition considered in the literature. Consequently, they do not admit numéraire portfolios or equivalent risk-neutral probability measures, which makes them unsuitable for contingent claim valuation. Unsurprisingly, the published option pricing formulae for such models violate classical no-arbitrage bounds.

Citation

Buckner, D., Dowd, K., & Hulley, H. (2024). Arbitrage problems with reflected geometric Brownian motion. Finance and Stochastics, 28(1), 1-26. https://doi.org/10.1007/s00780-023-00525-x

• Journal Article Type: Article
• Acceptance Date: Aug 23, 2023
• Online Publication Date: Dec 20, 2023
• Publication Date: Jan 1, 2024
• Deposit Date: Aug 24, 2023
• Publicly Available Date: Jan 4, 2024
• Journal: Finance and Stochastics
• Print ISSN: 0949-2984
• Electronic ISSN: 1432-1122
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 28
• Issue: 1
• Pages: 1-26
• DOI: https://doi.org/10.1007/s00780-023-00525-x
• Keywords: Local time, Contingent claim valuation, 91G15, C6, G12, 91G16, Arbitrage, G13, 60H10, Reflected geometric Brownian motion
• Public URL: https://durham-repository.worktribe.com/output/1724279